Now that I have finally stumbled across the basic physics (which the Consensus keeps well hidden) that tells you 99% of what you need to know about why there has to be a lapse rate (and hence why the sea level temperature is warmer than you'd expect from solar radiation alone) and how to calculate it (between 8K/km and 10K/km, depending on which method you use - water vapour and water droplets moderate that to the observed 6.5K/km lapse rate), lots of other things just fall into place.
The infamous IPCC 'world energy budget' diagram (scroll down here) shows that the troposphere is emitting twice as much IR radiation back down to the hard surface as it is radiating to space. So with a straight face, the Consensus segues into the claims that 'greenhouse gases' are trapping heat and/or actually reflecting it, in other words the IR bounces back and forth between hard surface and troposphere, the 'greenhouse gases' act like a layer of insulation etc.
This all seems very implausible to me. In any sane world, a hot object emits IR evenly in all directions. The Consensus are also confusing cause and effect - the lower layers aren't hotter because they are absorbing and hence emitting more radiation; they are hotter anyway because of the inevitable lapse rate, so of course they emit more radiation!
The effect is actually measurable though, so it's a question of finding the actual explanation. There is no point picking holes in a flawed explanation (I wasted far too much time and mental effort on that), just start again with the basic physics (and get cause and effect the right way round!).
The actual explanation is - as ever - quite simple.
We've already established that the actual surface of Earth is not the hard surface, it is the troposphere (and the top few inches of land or ocean that are part of the troposphere for calculation purposes). The average overall temperature of the troposphere is - unsurprisingly - the same as the 'effective temperature' (the temperature you can calculate on the basis of the amount of solar radiation coming in adjusted for albedo, on the assumption that there is no atmosphere). The temperatures lower down are higher and the temperatures higher up are lower than the effective temperature, because of the lapse rate.
So the troposphere at sea level is 288K. This is - according to the Consensus, and I am taking their word for it - emitting twice as much radiation (half of which hits the ground) as the layer of the troposphere that is high enough to be emitting radiation directly to space (half of which actually goes to space).
You can easily work out the temperature of the layer higher up that is emitting radiation to space, and then you can work out its likely altitude.
Just divide sea level temperature (= 288K) by the fourth root of 'double' (assuming the "twice as much" figure to be reliable) (= 1.19) = 242K.
How high is that layer?
Deduct 242K from 288K (= 46K) and divide that by the expected/calculated lapse rate (between 8K/km and 10K/km, call it 9K/km for sake of argument) = 5.1 km.
The Consensus figure is "about 5 km", so we are not far off!
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